A comprehensive simulation-optimization framework for pharmaceutical distribution networks

Safe, fast, punctual, energy-efficient, and comfortable rail traffic systems are important for rail operators, passengers, and the environment. Due to the increasing energy prices and environmental concerns, the reduction of energy consumption has become one of the key objectives for railway systems. On the other hand, with the increase of passenger demands in urban rail transit systems of large cities, it is important to transport passengers safely and efficiently. The main focus of the research presented in this thesis is to determine and develop mathematical models and solution approaches to shorten the travel time of passengers and to reduce energy consumption in railway systems. More specifically, the travel time of passengers has been considered in train scheduling, where passenger demands of urban rail transit systems are included. The energy efficiency has been taken into account both in the train scheduling and in the operation of trains. The main topics investigated in the thesis can be summarized as: • Optimal trajectory planning for a single train. We have considered the optimal trajectory planning problem for a single train under various operational constraints, which include the varying line resistance, variable speed restrictions, and the varying maximum traction force. The objective function of the optimization problem is a trade-off between the energy consumption and the riding comfort. We have proposed two approaches to solve this optimal control problem, namely a mixed-integer linear programming (MILP) approach and the pseudospectral method. Simulation results comparing the MILP approach, the pseudospectral method, and a discrete dynamic programming approach have shown that the pseudospectralmethod results in the best control performance, but that if the required computation time is also take into consideration, the MILP approach yields the best overall performance. • Optimal trajectory planning for multiple trains. The optimal trajectory planning problem for multiple trains under fixed block signaling systems and moving block signaling systems has been investigated. Four solution approaches have been proposed: the greedy MILP approach, the simultaneous MILP approach, the greedy pseudospectral approach, the simultaneous pseudospectral method. Simulation results have shown that compared to the greedy approach, the simultaneous approach yields a better control performance but requires a higher computation time. In addition, the end time violations of the MILP approach are slightly larger than those of the pseudospectral method, but the computation time of the MILP approach is one to two orders of magnitude smaller than that of the pseudospectral method. • Train scheduling for a single line based on OD-independent passenger demands. The train scheduling problem for an urban rail transit line has been considered with the aim of minimizing the total travel time of passengers and the energy consumption of the operation of trains. The departure times, running times, and dwell times of the trains have been optimized based on origin-destination-independent (OD-independent) passenger demands. We have proposed a new iterative convex programming (ICP) approach to solve this train scheduling problem. The performance of the ICP approach has been comparedwith other alternative approaches, such as nonlinear programming approaches, a mixed integer nonlinear programming (MINLP) approach, and an MILP approach. The ICP approach has been shown, via a case study, to provide the best trade-off between performance and computational complexity for the train scheduling problem. • Train scheduling for a single line based on OD-dependent passenger demands. We have adopted a stop-skipping strategy to reduce the passenger travel time and the energy consumption further based on origin-destination dependent (OD-dependent) passenger demands in an urban rail transit line. The train scheduling problem with stop-skipping results in a mixed integer nonlinear programming problem and we have proposed a bi-level optimization approach and an efficient bi-level optimization approach to solve this problem. Simulation results show that the stop-skipping strategy outperforms the all-stop strategy. Moreover, the bi-level approach yields a better control performance than the efficient bi-level approach but at a cost of a higher computation time. • Train scheduling for networks with time-varying OD-dependent passenger demands. For the train scheduling for urban rail transit networks, we have developed an event-driven model, where the time varying OD-dependent passenger demands, the splitting of passenger flows, and the passenger transfer behavior at transfer stations is included. The resulting train scheduling problem is a real-valued nonlinear nonconvex problem, which can be solved by gradient-free nonlinear programming approaches (e.g., pattern search), gradient-based nonlinear programming approaches (e.g., sequential quadratic programming (SQP)), genetic algorithms, or an MILP approach. We have applied an SQP method and a genetic algorithm to solve the train scheduling problem for a case study, the results of which have shown that the SQP method provides a better trade-off between control performance and computational complexity with respect to the genetic algorithm.

Algorithmic decision support for the construction of periodic railway timetables

Mitigating the risk of hazardous materials transportation: A hierarchical approach

Mixed Integer Linear Programming (MILP) has emerged as a powerful tool for optimizing complex supply chain networks. This paper explores the theoretical foundations of MILP, including the integration of integer variables and advanced solution techniques such as branch-and-bound and branch-and-cut algorithms. Through detailed modeling of production planning, network design, and transportation logistics, MILP enables companies to achieve significant cost reductions and operational efficiencies. We present case studies from retail, manufacturing, and pharmaceutical sectors to illustrate the practical applications of MILP. These examples demonstrate how MILP optimization can lead to reductions in production and inventory costs, improved customer satisfaction, and enhanced service levels. The findings underscore the value of MILP in addressing the multifaceted challenges of modern supply chain management.

Optimal network design constructs network topologies that minimize total network cost while allocating capacity and routing traffic to accommodate demand and performance requirements. Such problems are characterized by large dimensionality even when relatively small networks are considered. This work revisits discrete linear approaches and describes a network design model based on a Mixed Integer/Linear Programming (MILP) formulation that does not, as most other approaches, separate the link capacity assignment from routing and topological design but fully integrates these processes. An objective of the model is to achieve balanced network designs based on uniform utilization of resources. Performance requirements lead to the incorporation into the model of lower bound on link flows and restrictions on the maximum number of hops per route. The approach is general and can be applied to packet- and circuit-switched communication networks in the presence of upper bounds on capacity allocation. Numerical results based on the solution of an MILP problem using a standard package are presented here. A numerical solution of an exact small network problem is described and compared with heuristic techniques for reducing the MILP problem size, techniques which contribute to the solution of small- and medium-sized networks. To demonstrate the flexibility and broad coverage of this basic network design model, extensions in the area of traffic and trunk routing, as well as facility design and engineering, are presented.

Real-world decision-making problems often involve decision-dependent uncertainty, where the probability distribution of the random vector depends on the model’s decisions. Few studies focus on two-stage stochastic programs with this type of endogenous uncertainty, and those that do lack general methodologies. We propose a general method for solving a class of these programs based on random variable transformation, a technique widely employed in probability and statistics. The random variable transformation converts a stochastic program with endogenous uncertainty (original program) into an equivalent stochastic program with decision-independent uncertainty (transformed program), for which solution procedures are well studied. Additionally, endogenous uncertainty usually leads to nonlinear nonconvex programs, which are theoretically intractable. Nonetheless, we show that for some classical endogenous distributions, the proposed method yields mixed-integer linear or convex programs with exogenous uncertainty. We validate this method by applying it to a network design and facility-protection problem, considering distinct decision-dependent distributions for the random variables. Although the original formulation of this problem is nonlinear nonconvex for most endogenous distributions, the proposed method transforms it into mixed-integer linear programs with exogenous uncertainty. We solve these transformed programs with the sample average approximation method. We highlight the superior performance of our approach compared with solving the original program in the case that a mixed-integer linear formulation of this program exists. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This research was funded by Scale AI [the SCALE-AI Chair in Data-Driven Supply Chains], the Fonds de recherche du Québec [the FRQ -IVADO Research Chair], the IVADO [the FRQ -IVADO Research Chair], and the Natural Sciences and Engineering Research Council of Canada [Grant 2024-04051]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0847 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0847 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

ABSTRACTClosed-Loop Supply Chain (CLSC) network design plays a significant role in supply chain performance. The CLSC network design is recognized as a strategic problem which ensures a useful and efficient supply chain management providing an optimal platform. The CLSC network design problem includes two types of decisions, strategic and tactical. This paper aims to determine the location of facilities which is recognized as a strategic decision. In addition, tactical decisions such as the amount of supplied raw material, the level of production, and shipments among the network entities are made through the proposed model. This paper is distinctive by introducing a Mixed Integer Linear Programming (MILP)-based model which simultaneously optimizes the both forward and reverse chains. The model is implemented on a glass manufacturing industry to highlight the importance and applicability of the framework. Moreover, the study provides a comprehensive sensitivity analysis to investigate the effect of parameters such as demand and return rates on strategic and tactical decisions in supply chain network.

This paper proposes a novel mixed-integer linear programming (MILP) model for the expansion planning of active distribution networks, which not only is able to accurately reflect the fundamental characteristics of the problem, but also provides the opportunity to find its optimal solution in a computationally efficient manner. This model is able to jointly expand both the network assets (feeders and substations) and distributed generators (DGs) while minimizing the investment and operation costs and taking all the necessary physical and technical constraints into account. A highly accurate linearization method based on polyhedral approximation is utilized to eliminate the nonlinearities of AC power flow equations and obtain the proposed MILP model. Furthermore, a bi-level approach is also proposed to accelerate the solution process and reduce the computation time. This solution approach is comprised of a pre-solution level in which a simplified MILP model is solved to find a near-optimal initial solution for the expansion planning problem, and a main solution level in which the proposed accurate MILP model is solved considering the already found initial solution. Finally, a 24-node distribution system is used to verify the effectiveness of the proposed planning methodology.

A qualification management problem arising in semiconductor wafer fabrication facilities (wafer fabs) is discussed. The stepper equipment needs to be qualified to process lots that belong to different families. Stepper- and family dependent qualification time windows exist. Time windows can be reinitialized if required and can be extended by on-time processing of lots from qualified families. A hierarchical approach is proposed. The base-level provides a dispatching strategy that takes into account qualification decisions, while the mid-level consists of a mixed integer linear program (MILP) for making qualification decisions. The top-level comprises a linear program (LP) that computes target quantities for the families on the steppers in each period of the planning window taking into account fab-wide objectives. In addition to an LP formulation with conventional capacity constraints, we provide a formulation where clearing functions are used to represent the congestion of the wafer fab. We also discuss how to anticipate the behavior of the mid-level on the top-level. Results of simulation experiments where the hierarchical approach is applied in a rolling horizon manner demonstrate that the LP-based approaches outperform a heuristic to determine the target quantities. Among the LP formulations, the ones with clearing functions perform best. We also demonstrate the value of anticipation. Note to Practitioners—A hierarchical approach is designed to decide when tools in wafer fabs have to be qualified for a certain lot family. Qualification-related decisions are highly relevant because qualifications are costly and take a lot of time. The top-level determines target quantities for each family based on linear programming. The mid-level is formed by a MILP. A dispatching scheme to implement the qualification decisions provides the base-level. The hierarchical approach is assessed in a rolling horizon setting using a simulation model of a 200mm wafer fab. The benefit of the different levels of the hierarchy is demonstrated by simulation experiments.

We consider an IP/MPLS-over-WDM overlay network, which an IP/MPLS service layer exists independently over a WDM transport network. In the overlay model, two adjacent layers communicate with each other only through a pre-defined user-network interface (UNI) and the WDM topology information is not available to the service layer. In this paper, we concentrate on network design with a fault tolerance mechanism provided only in the IP/MPLS service layer in which the label-switched path (LSP) protection takes into account both node failures in the IP/MPLS service layer and failures in the WDM transport layer. In this design problem, the service layer must decide how lightpaths or logical links should be provisioned and how primary and backup LSPs should be routed in a cost-effective manner, such that failures do not affect both LSPs simultaneously. We formulate this survivable IP/MPLS overlay network design problem as a mixed integer linear program (MILP). Since the MILP is computationally intractable for large networks, we solve it only for a small network and present the optimal solution found by CPLEX 7.5, a commercial MILP solver. In order to find efficient solutions in larger networks we propose a heuristic algorithm that performs near-optimally in the cases studied. we then compare total costs for LSP protection from WDM link failures and LSR failures may not be much more expensive than protection from LSR failures only.

A comparison of two energy management systems for an isolated microgrid based on photovoltaic generation is presented in this paper. One energy management system is presented as an optimization problem solved by means of a mixed integer linear programming which aims to minimize the operating cost of the microgrid. The algorithm determines the optimal power dispatch of all distributed generation units using reduced linear models and operating constraints for each unit, together with a cost function, and historical information of meteorological and demand conditions. The simulation of the microgrid is carried out in Matlab. Results from the mixed integer linear programming are compared with results obtained from a proposed weighted algorithm, showing a reduction in the operating cost of the microgrid when the mixed integer linear programming algorithm is used; however, this algorithm spent more processing time than the weighted algorithm.

Artificial Islands are often an effective strategy to develop shallow-water fields. However, their layout and design are affected by numerous drilling and surface facility constraints, such as water depth, number of wells, proximity to shore, and well spacing. When these constraints cannot be honored, conventional offshore wellhead platforms must be installed instead. This paper reviews previous artificial island projects to identify their key constraints, and then proposes a numerical model that accounts for these constraints when determining whether artificial islands or offshore platforms would generate the highest Net Present Value (NPV) configuration. The model uses a combination of discrete and continuous mathematical algorithms to find the optimum development plan in shallow-water fields. Specifically, the model analyses the water depth, drilling and surface facilities of the field to suggest the optimum facility type to drill the wells using a k-means algorithm and Mixed-Integer Linear Programming (MILP). Then, a local optimization routine is used to connect islands to well targets. The model accounts for limitations on well spacing and the well paths to ensure that wells conform to the available drilling-rig capabilities and well-pad design requirements. The overall field configuration is optimized using a stochastic-perturbation method that adjusts the field network to maximize the NPV of the development. The model explores the numerous possible scenarios that exist when planning shallow-water offshore field developments, especially when a high number of wells is required. The coupling of continuous and discrete optimization techniques provides a quick and effective method to analyze these possible scenarios and select an optimal strategy. Results from the model indicate that offshore wellhead platforms are not always favored over artificial islands in offshore field developments, particularly when extended reach wells are present. This is illustrated with a case study that demonstrates each stage in the integrated model starting from the analysis of the reservoir simulation model, through to well planning, and design of the facility network. The study highlights how such integrated analysis can aid in the selection of the highest development NPV plan in shallow-water fields by not only minimizing the cost associated with the development but also reducing the time required to generate the optimum plan.

Minimum cost dimensioning of ring optical networks

Reverse logistics has become an important entity in the world economy. Nonetheless, many companies are not capable of or are unwilling to enter the reverse logistics market. Such reluctance appears to be attributed to lack of knowledge of reverse logistics. With the emergence of new type of electronic product, it brings a lot of electronic wastes. There are lots of deleterious materials in these wastes, they must be disposed well, and otherwise, they will do great harm to environment. Meanwhile, there is high recyclable and reusable value in these wastes. So the recycling problem of electronic waste has brought the attention of every country in the world. Especially in the field of design of recycling network, some researchers have studied in both the theoretical and practical field. Collection and recycling of product returns is gaining interest in business and research worldwide. In this paper, we provide an integrated holistic conceptual framework that combines descriptive framework. We also provide detailed solutions for network configuration and design and the MILP(Mixed Integer Linear Programming) model whose objective function is the lowest cost of the network is built. According to the characteristic of the model, the software of Lingo 8.0 is applied to solve the model. Considering the relationship between the scope of electronic waste recycling network and recycling quantities, recycling quantity are calculated.

This work is about mission planning in teams of mobile autonomous agents. We consider tasks that are spatially distributed, non-atomic, and provide an utility for integral and also partial task completion. Agents are heterogeneous, therefore showing different efficiency when dealing with the tasks. The goal is to define a system-level plan that assigns tasks to agents to maximize mission performance. We define the mission planning problem through a model including multiple sub-problems that are addressed jointly: task selection and allocation, task scheduling, task routing, control of agent proximity over time. The problem is proven to be NP-hard and is formalized as a mixed integer linear program (MILP). Two solution approaches are proposed: one heuristic and one exact method. Both combine a generic MILP solver and a genetic algorithm, resulting in efficient anytime algorithms. To support performance scalability and to allow the effective use of the model when online continual replanning is required, a decentralized and fully distributed architecture is defined top-down from the MILP model. Decentralization drastically reduces computational requirements and shows good scalability at the expenses of only moderate losses in performance. Lastly, we illustrate the application of the mission planning framework in two demonstrators. These implementations show how the framework can be successfully integrated with different platforms, including mobile robots (ground and aerial), wearable computers, and smart-phone devices.